A spatial interaction incorporated betweenness centrality measure.

Betweenness centrality (BC) is widely used to identify critical nodes in a network by exploring the ability of all nodes to act as intermediaries for information exchange. However, one of its assumptions, i.e., the contributions of all shortest paths are equal, is inconsistent with variations in spatial interactions along these paths and has been questioned when applied to spatial networks. Hence, this paper proposes a spatial interaction incorporated betweenness centrality (SIBC) for spatial networks. SIBC weights the shortest path between each node pair according to the intensity of spatial interaction between them, emphasizing the combination of a network structure and spatial interactions. To test the rationality and validity of SIBC in identifying critical nodes and edges, two specific forms of SIBC are applied to the Shenzhen street network and China's intercity network. The results demonstrate that SIBC is more significant than BC when we also focus on the network functionality rather than only on the network structure. Moreover, the good performance of SIBC in robustness analysis illustrates its application value in improving network efficiency. This study highlights the meaning of introducing spatial configuration into empirical models of complex networks.